Frequency estimation is the cornerstone of digital signal processing, whether for analysis of radar, sonar, speech, or telephony signals. The Fourier transform, embodied in the modern FFT algorithm, has been the leading method of frequency estimation both in hardware and software. Twenty years before the advent of the FFT, Gabor introduced the notion of Instantaneous Frequency (IF) for a signal, which is derived from a complex extension using the Hilbert transform. The critical property that allowed such a different approach is the orthogonality of any signal to its Hilbert transform; Gabor's IF notion applied ideas from classical complex analysis.
The Fourier transform suffers from the well-known localization constraint, an inability to resolve time and frequency equally well, while the Hilbert transform is an infinite impulse response (IIR) filter, hence realizable digitally only approximately.
Typical of prior art methods employing the Fourier transform to estimate frequency include:
U.S. Pat. No. 4,904,930, entitled “ESTIMATION OF CARRIER FREQUENCY ESTIMATION,” U.S. Pat. No. 5,729,124, entitled “ESTIMATION OF SIGNAL FREQUENCY USING FAST WALSH TRANSFORM,” and U.S. Pat. No. 6,577,968 entitled “METHOD OF ESTIMATING SIGNAL FREQUENCY,” each disclose a method of estimating frequency using the either a Fourier transform or a Walsh-Hadamard transform, a generalized class of Fourier transforms. The present invention does not use Fourier or Walsh transforms, as do the methods described in U.S. Pat. Nos. 4,904,930, 5,729,124, and 6,577,968. U.S. Pat. Nos. 4,904,930, 5,729,124, and 6,577,968 are hereby incorporated by reference into the specification of the present invention.
There exists a need to estimate frequency of a signal in a less computationally complicated manner.